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United States Patent |
5,276,614
|
Heuscher
|
January 4, 1994
|
Dynamic bandwidth reconstruction
Abstract
A scanner (A), such as a CT or MR scanner, non-invasively examines a region
of interest of subject and generates a plurality of views indicative
thereof which are reconstructible into an image representation. A filter
control (14) generates a bandwidth scaling factor (BWF.sub..theta.) and a
bandwidth offset (BWO) for each view. Preferably, the selected bandwidth
scaling factor is the maximum of a plurality of bandwidth scaling factors
based on different criteria including noise, missing views, material
surrounding the region of interest, or noise texture. The bandwidth
scaling factor is then used to address a filter curve look up table (18)
to select from a plurality (N.sub.T) of filter values. The digital filter
values are interpolated (20) or extrapolated as necessary to match the
number of values (N.sub.S) in each sampled view. The digital filter values
and the view values are multiplied (22) point by point to create filtered
views which are reconstructed (30) into the image representation for
storage in an image memory (32) or displayed on a video monitor (34).
Inventors:
|
Heuscher; Dominic J. (Aurora, OH)
|
Assignee:
|
Picker International, Inc. (Highland Hts., OH)
|
Appl. No.:
|
438687 |
Filed:
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November 17, 1989 |
Current U.S. Class: |
382/260 |
Intern'l Class: |
G06F 015/00 |
Field of Search: |
364/413.16,413.21,413.23,413.14,724.05
382/54,6
358/111
|
References Cited
U.S. Patent Documents
4288695 | Sep., 1981 | Walters et al. | 378/5.
|
4305127 | Dec., 1981 | Heuscher | 364/414.
|
4333145 | Jun., 1982 | Heuscher et al. | 364/414.
|
4707786 | Nov., 1987 | Dehner | 364/413.
|
4712178 | Dec., 1987 | Tuy et al. | 364/413.
|
4714997 | Dec., 1987 | Crawford et al. | 364/414.
|
4716368 | Dec., 1987 | Haacke | 324/309.
|
4761819 | Aug., 1988 | Denison et al. | 382/54.
|
4792900 | Dec., 1988 | Sones et al. | 364/413.
|
4887306 | Dec., 1989 | Hwang et al. | 382/54.
|
4979111 | Dec., 1990 | Nishimura | 364/413.
|
5065444 | Nov., 1991 | Garber | 382/54.
|
Foreign Patent Documents |
0242909 | Jul., 1986 | EP.
| |
2547149 | Sep., 1987 | FR.
| |
Other References
Convolution Algorithms for Arbitrary Projection Angles by Mark E. Davison
and F. A. Grunbaum, IEEE TRans. on Nuc. Sci., vol. NS-26, No. 2, Apr.
1979.
|
Primary Examiner: Envall, Jr.; Roy N.
Assistant Examiner: Chung; Xuong
Attorney, Agent or Firm: Fay, Sharpe, Beall, Fagan, Minnich & McKee
Claims
Having thus described the preferred embodiment, the invention is now
claimed to be:
1. A diagnostic imaging apparatus comprising:
a scanner for generating a plurality of views for reconstruction into an
image representation of an examined subject, each view including a set of
data corresponding to a different angular orientation around the subject,
each view being identified by a corresponding view identification, the
view identification being identifying the angular orientation
corresponding to the data set of each view;
a filter-function providing means for providing a plurality of filter
functions for each view in accordance with the view identification, at
least one or more of the filter functions changing from view to view;
a filter control means operatively connected with the scanner to receive
the view identification of each view and with the filter function
providing means for dynamically selecting one of the plurality of filter
functions provided in accordance with each received view identification;
a filter means operatively connected with the scanner and the filter
control means to receive concurrently each view and the one of the
plurality of filter functions selected for the received view for filtering
each received view with the filter function selected for the each received
view;
a reconstruction means operatively connected with the filter means for
reconstructing an image representation from the filtered views.
2. A diagnostic imaging apparatus comprising:
a scanner for generating a plurality of views for reconstruction into an
image representation;
a filter control means for dynamically selecting at least one of a
bandwidth scaling factor and a bandwidth offset for each generated view;
a filter function look up table which is addressed by the selected at least
one of the bandwidth scaling factor and the bandwidth offset from the
filter control means to retrieve a corresponding one of a plurality of
filter functions the filter function look-up table being connected with
the filter control means;
a filter means for filtering each view with the retrieved filter functions,
the filter means being operatively connected with the scanner and the
filter function look up table;
a reconstruction means for reconstructing an image representation from the
filtered views, the reconstruction means being connected with the filter
means.
3. The apparatus as set forth in claim 2 wherein each view has a first
plurality of digital data values and the filter functions stored by the
filter function look up table have a smaller plurality of digital filter
values and further including an interpolating means for interpolating the
filter values such that the filter function has the same number of digital
values as each view, the interpolating means being operatively connected
with the filter means.
4. The apparatus as set forth in claim 3 wherein the filter means includes
a multiplying means for multiplying the interpolated filter values and the
data values point by point.
5. The apparatus as set forth in claim 2 wherein the filter control means
includes at least one of:
a noise filter providing means for providing bandwidth scaling factors for
compensating for noise;
a missing view filter providing means for providing bandwidth scaling
factors to compensate for missing views;
a noise texture filter providing means for providing bandwidth scaling
factors for adjusting noise texture.
6. The apparatus as set forth in claim 2 wherein the filter control means
includes a plurality of bandwidth filter function providing means for
providing a plurality of bandwidth scaling factors for each view, the
bandwidth scaling factors varying from view to view.
7. The apparatus as set forth in claim 7 wherein the bandwidth filter
function providing means include at least two of:
a noise filter providing means for providing a view dependent bandwidth
scaling factor for compensating for noise;
a missing view filter providing means for providing bandwidth scaling
factors to compensate for missing views;
a noise texture filter means for providing a bandwidth scaling factor for
adjusting noise texture;
a means for providing an out of region of interest material bandwidth
scaling factor which adjusts the bandwidth of selected views to
accommodate material adjacent an imaged region of interest.
8. A diagnostic imaging apparatus comprising:
a scanner for generating patient data including a plurality of views for
reconstruction into an image representation of an imaged region;
a filter selecting means for selecting one of a plurality of filter
functions, the filter functions including at least two of (i) a noise
filter, (ii) a view dependent adjacent high density material filter which
compensates for high density structures adjacent the imaged region, (iii)
a view dependent noise texture filter, and (iv) a missing view filter
function for weighting views interpolated to replace missing views and
views adjoining the missing views;
a filter means for operating on each view with the selected filter
function;
a reconstruction means for reconstructing an image representation from the
filtered views.
9. A method of generating an image representation, the method comprising:
non-invasively examining an interior portion of a subject within an
examination region and generating patient data including a plurality of
views indicative thereof for reconstruction into an image representation
of the examined region;
providing an identification of each view;
receiving each provided identification and providing a plurality of
corresponding view dependent filter functions for each view such that the
plurality of provided filter functions varies from view to view;
in response to each view identification, selecting one of the plurality of
provided filter functions;
filtering each view with the selected one of the plurality of provided
filter functions;
reconstructing the filtered views into the image representation.
10. A method of generating an image representation, the method comprising:
non-invasively examining an interior portion of a subject within an
examination region and generating patient data including a plurality of
views indicative thereof for reconstruction into an image representation
of the examined region;
storing at least one of a bandwidth scaling factor and a bandwidth offset
for each view;
addressing a filter function look up table with the one of the bandwidth
scaling factor and offset to retrieve a corresponding filter function
therefrom;
operating on the patient data with the addressed filter function of the
corresponding view;
reconstructing the views which have been operated on by the addressed
filter function into the image representation.
11. The method as set forth in claim 10 further including:
storing a plurality of bandwidth scaling factors for each view; and,
comparing the plurality of bandwidth scaling factors with a preselected
criterion and selecting one of the bandwidth scaling factors to address
the look up table in accordance with the comparing.
12. The method as set forth in claim 16 wherein the plurality of bandwidth
scaling factors compensate for at least two of noise, missing views,
material surrounding the region of interest, and noise texture.
13. A method of generating an image representation, the method comprising:
non-invasively examining an interior portion of a subject within an
examination region and generating patient data including a plurality of
views indicative thereof for reconstruction into an image representation
of the examined region;
selecting a filter function for each view from among a plurality of filter
functions including at least two of:
a noise filter function for correcting for noise,
a missing views filter function for correcting for missing views, a
surrounding material filter function for correcting for material
surrounding the region of interest, and
a noise texture filter function for correcting for noise texture;
operating on each view the patient data with the selected filter function
selected for that view;
reconstructing the filtered views into the image representation.
14. A diagnostic imaging apparatus comprising:
a scanner for generating a plurality of views, each view including a real
component and an imaginary component;
a filter control means for dynamically selecting (i) one of a plurality of
real bandwidth factors for each view and (ii) one of a plurality of
imaginary bandwidth factors for each view, on a view-by-view basis;
a filter function look up table means which is addressed by the real and
imaginary bandwidth factors to retrieve corresponding real and imaginary
filter functions, the filter function look up table means being
operatively connected with the filter control means;
a filter means for filtering the real component of each view with the
retrieved real filter function and for filtering the imaginary component
of each view with the retrieved imaginary filter function, the filter
means being operatively connected with the scanner to receive the real and
imaginary component of each view therefrom and with the filter function
look up table means for receiving the retrieved real and imaginary filter
functions therefrom; and
a reconstruction means for reconstructing an image representation from the
filtered real and imaginary components, the reconstruction means being
operatively connected with the filter means to receive the filtered real
and imaginary components therefrom.
Description
BACKGROUND OF THE INVENTION
The present invention relates to the art of image reconstruction. It finds
particular application in conjunction with CT scanners and will be
described with particular reference thereto. However, it is to be
appreciated that the present invention is also applicable to the
reconstruction of images from magnetic resonance data, digital x-ray data,
PET data, and the like.
A CT scanner generates lines or views of image data values. The data values
of each view commonly represent radiation attenuation along rays of a fan
shaped swatch through a slice of a patient. Different views represent the
same fan shaped swatch but at different angular orientations about the
patient. The views of data are collected in a data memory and
reconstructed into an image representation, most commonly by a process of
convolution and backprojection, also known as filtered backprojection. By
filtering all the views with a common filter, image artifacts, noise
degradation, and the like can be reduced or eliminated. Conventionally,
all views are filtered with the same filter function.
In U.S. Pat. No. 4,333,145, only some data is filtered prior to the
reconstruction. The data collected from rays which pass through the
patient's arm pass through more bone than other rays giving that data a
different bandwidth. The '145 patent filters only the rays of data that
pass through the patient's arms with a preselected fixed filter function
to reduce or eliminate bandwidth related artifacts in the resultant image.
Data from other scanners has also been filtered either as the data is
collected or reconstructed into an image representation. However, such
filtering again tends to be fixed for a given image.
The present invention contemplates a new and improved filtering technique
which overcomes the above referenced problems and others.
SUMMARY OF THE INVENTION
In accordance with one aspect of the present invention, a scanner generates
data views for reconstruction into an image representation. A filter means
filters each of the views with one of a range of filter functions. A
filter control means selects among the range of filter functions on a
view-by-view basis. A reconstruction means reconstructs an image
representation from the filtered views.
In accordance with another aspect of the present invention, the filter
control means includes an adaptive filter means for selecting a view
dependent filter function such as on the basis of one or more of: the
noise of each view, missing views, material adjacent the region of
interest, and a noise texture filter function. A comparing means compares
filter functions selected on two or more of these bases with preselected
criteria and controls the filter means in accordance with a selected one
of the filter functions. In the preferred embodiment, the comparison
criteria is based upon the filter function which provides the most
filtering.
In accordance with another aspect of the present invention, a method of
generating image representations is provided. A plurality of views of data
are generated for reconstruction into an image representation. Each view
is filtered with a filter function. A filter function is selected for each
view which provides optimal filtering for each view. The uniquely filtered
views are reconstructed into the image representation (e.g. two
dimensional uniformity).
In accordance with a more limited aspect of the present invention, the
filter controlling criteria is based on noise equalization, bandwidth
correction for missing views, known system or image constraints, or noise
texture.
In accordance with a still more limited aspect of the present invention,
filter functions for a plurality of corrections are determined and the
filter function which provides the greatest filtering is selected.
One advantage of the present invention is that it optimizes the filter
function for each of the multiplicity of views of a reconstructed image.
Another advantage of the present invention is that it reduces artifacts in
the resultant image.
Still further advantages of the present invention will become apparent to
those of ordinary skill in the art upon reading and understanding the
following detailed description.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention may take form in various parts and arrangements of parts or
in various steps and arrangements of steps. The drawings are only for
purposes of illustration and are not to be construed as limiting the
invention.
FIGS. 1A and 1B taken together are a diagrammatic illustration of the
present invention;
FIG. 2 illustrates a range of filter function adjustments for an exemplary
low pass filter function.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
A scanner A such as a CT scanner, magnetic resonance scanner, PET scanner,
digital x-ray scanner, or the like non-invasively examines a region of
interest, e.g. a slice or volume, of a subject in an examination region.
The scanner generates views of data, each view indicative of a property of
the region of interest and identifications of each view. In a third
generation CT scanner, each view is a series of data values that
correspond to an arc of radiation detectors which rotate about a scan
circle with a radiation source. The detectors are resampled each time the
source and detectors rotate an incremental angular distance to produce
additional views of data. In a magnetic resonance scanner, each view
includes data values corresponding to each of a spectrum of frequencies
sampled with one of a plurality of phase encodings. The data generation is
repeated with each of the phase encodings to generate the plurality of
views. In a fourth generation scanner, radiation detectors are mounted
stationarily around the scan circle. Each detector is sampled a
multiplicity of times as the x-ray source rotates around the scan circle
from the detector. Each view corresponds to the samplings of a single
detector as the radiation source rotates behind the scan circle. Each of
the multiplicity of detectors provides one of the plurality of views.
A filter means B selects and filters each view with a corresponding filter
function to compensate for one or more of noise, missing views, high
density objects, noise texture, or the like. An image reconstruction means
C reconstructs the uniquely filtered views into an image representation.
Looking more specifically to the filter means B, the data is stored in a
view memory means 10 in accordance with the view designations. A missing
data interpolating means 12 interpolates adjacent data to replace the data
of any missing views or other missing data. The interpolated data is
returned to the view memory 10 to fill the memory cells left empty by the
missing data. The interpolating means 12 also provides an indication of
the interpolated views or other interpolated data to a filter control
means 14.
A read out means 16 serially reads each view of N.sub..theta. sampled
views from the view memory 10. Alternately, the memory 10 may be a buffer
or the like through which the views pass serially for pipeline processing.
As each view is read out, the filter control means 14 designates a
corresponding filter function for filtering the read view. More
specifically to the preferred embodiment, the filter control means
generates a bandwidth scaling factor BWF.sub..theta. or other filter
designation which addresses a filter function or curve look up table 18
which stores a digital description of each of a range of selectable filter
functions or curves. The filter functions include a notch filter, low pass
filter, high pass filter, band pass filter, or the like. Preferably, these
filters are based on cosine functions. Various other filter functions may,
of course, also be utilized.
The filter table 18 stores a limited number of points or values N.sub.T of
the filter curve. An interpolating means 20 interpolates between the
stored filter points, e.g. a linear interpolation, to expand the filter
function to as many values as the number of data values of the sampled
views N.sub.S. A multiplying means 22 multiplies each filter function
point by point with the corresponding view. When the read out means 16
reads out the next view, the filter function control means 14 determines
the appropriate bandwidth scaling factor for that view and addresses the
filter look up table 18. In this manner, the filter function is
automatically selected individually for each view.
Commonly, each view includes real and imaginary components, also called
sine and cosine or in-phase and out-of-phase components. The read out
means 16 reads out the two data components for each view individually. The
first filter control means 14 determines the appropriate filter for the
real component and a second filter control means 14' determines the
appropriate filter for the imaginary component. A second filter selection
means 14' selects a second bandwidth scaling factor which accesses a
second filter curve table 18' to retrieve the values of the selected
filter curve. A second interpolating means 22' interpolate the filter
curve to N.sub.S values such that a second multiplying means 24 can
multiply each of the N.sub.S data values by a corresponding filter value.
The image reconstruction means C includes a reconstruction algorithm 30.
For CT scanners, a conventional convolution and backprojection or filter
backprojection algorithm may be utilized. For magnetic resonance imagers,
an inverse two dimensional Fourier transform algorithm is commonly
utilized. Other conventional reconstruction algorithms may be selected in
accordance with the type of scanner and the nature of the diagnostic
procedure. The reconstruction means accumulates the reconstructed data in
an image memory 32 until all the views have been processed to form a
complete electronic image representation. Each image representation may be
selectively read from the image memory and displayed on a video monitor
34. Various post processing techniques may be utilized to improve the
quality of the image in the image memory 32. The enhanced or raw image
representations may also be stored on tape or disk, subject to other
processing, or the like.
In filtered backprojection, the views of data are operated upon with a
filter function. Part of this filtering operation may be incorporated in
the filtering means B. The reconstruction filter may in whole or in part
be combined with the filter curves stored in the filter curve look up
table 18 such that the point by point multiplying means 22, 22' perform
part of the reconstruction algorithm. Optionally, a multiplying means 36
may multiply the interpolated or extrapolated filter function 20 by a
system kernal 38. Analogous filter-like portions of other reconstruction
algorithms may also be shifted from reconstruction means C to filter means
B.
In the preferred embodiment, the filter control means 14, 14' select the
filter function for each view based on several criteria. Because filter
control means 14 and 14' are of substantially identical construction,
filter control means 14 is described in detail herein below and is to be
appreciated that the description applies analogously to both. The filter
control means includes an adaptive noise equalization filter selecting
means 40 for selecting an appropriate filter function in accordance with
the noise of each processed view. The noise may be assessed based on the
noise of the preceding view, noise from a corresponding view of a
preceding slice or scan, or the like. Alternately, the entire set of view
data may be collected in view memory 10 before further processing is
commenced such that the noise filter selecting means selects the noise
filter based on the actual noise of the scan and each view.
A missing views bandwidth correction filter means 42 selects an appropriate
filter for adjacent views that have been created by interpolation. That
is, interpolated views have a lower bandwidth than actually collected
views and may have additional noise from one of the interpolated views.
The missing view bandwidth correction filter selection means 42 selects a
bandwidth scaling factor that retrieves a larger, narrower bandwidth
filter for the interpolated view. The bandwidth scaling factor selected
for adjoining views also retrieves filter functions with a reduced
bandwidth, but less reduced than for the missing view.
A predefined bandwidth correction means 44 selects a bandwidth scaling
factor to compensate for high density objects or other materials adjacent
the region of interest. The filter may be selected in accordance with the
angular position of a CT scan view as in U.S. Pat. No. 4,333,145, may be
based on data derived from the view memory 10, information from an
unfiltered pilot reconstruction, or the like.
A noise texture filter means 46 selects bandwidth scaling factors which
address filter functions which varies with angular position around the
scan circle to provide a noise texture that is more desirable. More
specifically, reconstructions based on a circularly symmetric 2-D kernel
tend to have circularly symmetric noise texture which can be
disconcerting. The noise texture filter selection means selects
appropriate angularly dependent filter functions to stretch the noise
texture at the corners into a closer approximation of a square or
rectangular display.
Additional filter function selection means 48 may also be provided for
selecting a filter function based on other criteria. A selection means 50
compares each of the bandwidth scaling factors designated by the filter
function selection means 40-48 with preselected criteria and passes one of
them as the address to the filter look-up table 18. In the preferred
embodiment, the filter curve comparing means 50 selects the maximum filter
function for each view, i.e. passes the smallest bandwidth.
With reference to FIG. 2, a typical low pass filter function 60 is
illustrated. The shape of this curve is adjusted as illustrated at 62 to
adjust the frequency range over which the function is applied. Curve 62
has a different slope than filter curve 60 and therefore a wide bandwidth.
In addition to rescaling the filter function, the filter function may also
be shifted by an offset as illustrated by filter curve 64. Filter curve 64
is essentially the same as curve 60 but shifted to cut off a smaller range
of frequencies. With these two control factors, the filter function can be
varied over a wide range such as the very narrow frequency range of filter
curve 66 or the almost all inclusive frequency range of filter curves 68
and 70.
The look-up table 18 defines the shape of the band limiting filter function
to be used in the frequency or Fourier domain, i.e. before reconstruction.
The filter function control means 14 selects a bandwidth scale factor
BWF.sub..theta. which defines the frequency range over which the filter
function is to be applied and a bandwidth offset BWO which defines a
center or other characteristic frequency of the selected filter function.
The bandwidth scale factor varies from a value of zero corresponding to no
band limiting, i.e. all values for the apodized function become mapped
into the DC value, to an arbitrarily large factor corresponding to extreme
low pass filtering to a filter value where only DC or an averaged data
value is passed. Expressed mathematically, the apodized function is
expressed as:
A.sub..theta. (f)=T.sub.I (O) for BWF.sub..theta. =0 (1a)
A.sub..theta. (f)=T.sub.I (f.multidot.BWF.sub..theta.) for
0.ltoreq.f<N.sub.T /BWF.sub..theta. (1b)
A.sub..theta. (f)=T.sub.I (N.sub.T) for f.gtoreq.N.sub.T /BWF.sub..theta.
(1c),
where:
T.sub.I (O) is the value interpolated by the interpolating means 20 from
the bandwidth table 18 which contains N.sub.T +1 values;
BWF.sub..theta. is the bandwidth scale factor as a function of the view
designation .theta.;
for sampled, real functions, f assumes the values of f=0, .DELTA.f,
2.DELTA.f, . . . f.sub.N, where .DELTA.f=f.sub.N /N.sub.S ;
f.sub.N is the nyquist frequency of the sampled function whose spectrum is
computed with a 2N.sub.S sample (real) discrete Fourier transform.
The bandwidth factor BWF.sub..theta. is defined as a function of .theta.
which in computed tomography is the projection angle. The bandwidth or
resolution can be varied as a continuous function of the projection angle
.theta.. In CT, the bandwidth is sampled over N.sub..theta. discrete
views. In a fourth generation CT scanner, the number of views corresponds
to the number of detectors. In a third generation system, the number of
views is determined by the number of x-ray source positions at which the
detectors are sampled. In the CT scanner embodiment, the
convolution-backprojection reconstruction performed by the reconstruction
means 30 can be expressed mathematically as:
ALG.sub..theta. (f)=ALG.sub.p (f).multidot.A.sub..theta. (f)(2),
where f=0, .DELTA.f, 2.DELTA.f, . . . f.sub.N ; and, ALG.sub.p is the
predefined system convolution kernel for convolution-backprojection. When
no non-linear phase corrections are performed, these are real functions
and are used to multiply the complex Fourier data in performing a Fourier
convolution:
CD.sub..theta. (f)=D.sub..theta. (f).multidot.ALG.sub..theta. (f)(3a)
=D.sub..theta. (f).multidot.[ALG.sub.p (f).multidot.A.sub..theta. (f)](3b),
where D.sub..theta. (f) is the Fourier transform of the projection at angle
.theta.; ALG.sub..theta. (f) is the algorithm to be applied at angle
.theta.; and CD.sub..theta. (f) is the Fourier transform of the convolved
projection at angle .theta.. Because D.sub..theta. is complex, the result
CD.sub..theta. (f) is also complex. In this manner, ALG.sub..theta. (f) is
defined by a single bandwidth scale factor BWF.sub..theta. which enables
the above discussed view angle dependent corrections of selecting means
40, 42, 44, and 46 to be incorporated concurrently into a CT
reconstruction.
In order to combine the bandwidth filter generation with the reconstruction
kernel, the algorithm in look up table 18 is divided into two classes. In
the first class (for .DELTA.f*BWF.sub..theta. <1), the output values
A.sub..theta. (f) are generated by a linear progression for each new table
value read in. This results in a very efficient inner loop. The second
class (for .DELTA.f*BWF.sub..theta. .gtoreq.1), most values are generated
by extrapolating points T(N.sub.T) for values corresponding to points
beyond the limit N.sub.T of the table. Extrapolation becomes necessary
because the number of points in the table N.sub.T is preferably
significantly smaller than the number of sampled data points N.sub.S. The
points within the scope of the table, as discussed above, are generated by
linear interpolation. It might be noted that when the multiplications of
Equation (2) and (3b) are performed while generating the interpolation
and/or extrapolation values, the amount of time added for the view
dependent filtering becomes negligible, i.e. there is virtually no cost in
reconstruction time.
The bandwidth offset defines the center, cut-off, or other characteristic
frequency of the selected filter function. In the preferred embodiment,
the selected filter function with the BWF.sub..theta. scaling factor has
a preselected cut-off frequency. The filter selecting means may also
designate an offset frequency, BWO, which is added or subtracted from the
preselected frequency to shift the bandwidth of the filter function.
Looking now in greater detail to the adaptive noise equalization bandwidth
scale factor selecting means 40, adaptive noise equalization provides for
a uniform distribution of noise statistics in a reconstructed object, even
substantially asymmetric objects. In many applications, it is
advantageous, for good low contrast detectability, to obtain uniform noise
statistics throughout the object. To accomplish this with the dynamic
bandwidth algorithm described above, a bandwidth scale factor is generated
which corrects for the nominal variation in noise as a function of
projection angle. It is to be appreciated that the noise statistics in CT
are principally based on x-ray-photon statistics.
The bandwidth factor is related to the power spectrum or noise factor by
the relationship:
Noise factor.sub.BW .apprxeq.1/[BWF(.theta.)*N.sub.S /N.sub.T +1](4).
In CT, the noise power spectrum is proportional to the prelogarithmic
attenuation. From the sampled data, an estimate A.sub.m (.theta.) of the
maximum attenuation at angle .theta. is obtained for all .theta.. A.sub.o
then represents the minimum value of all A.sub.m (.theta.). That is:
Noise factor.sub.A .apprxeq.e.sup.(A m.sup.(.theta.)-A o.sup.) (5).
For the bandwidth correction factor to adjust for the attenuation noise
factor,
Noise factor.sub.A .multidot.Noise factor.sub.BW .apprxeq.1=unity noise
factor (6).
Thus, the noise filter selection means 40 determines for each .theta. the
bandwidth scale factor BWF(.theta.) by the equation:
BWF(.theta.)=[e.sup.(A m.sup.(.theta.)-A o.sup.) -1].multidot.N.sub.T
/N.sub.S (7).
It may be noted that Equation (7) guarantees that BWF(.theta.) is always
greater than or equal to zero, i.e. assumes no negative values.
Looking to the missing view filter function selecting means 42, the regions
with missing views can be considered as being undersampled with respect to
the projection angle .theta.. In fourth generation CT scanners, missing
views generally correspond to bad detectors or detector modules.
Accordingly, a formula for the bandwidth scale factor is readily
determined given the number and location of the missing views. As an
example for one missing view, the bandwidth scale factor of 2N.sub.T
/N.sub.S satisfies the view sampling requirement for the extrapolated
missing view; whereas, adjacent views would have a bandwidth selection
factor of about N.sub.T /N.sub.S ; and all other views (assuming no other
missing views) would have a factor of zero, i.e. no filtering. Because the
number of missing views is usually very small compared with the total
number of views, view missing related artifacts are eliminated with no
measurable impact on resolution.
The high density object bandwidth filter selecting means 44 in a simplest
case may change the bandwidth scale factor between zero as views through
the patient's body are taken and a preselected value for views through the
patient's arms. Alternately, the high density object bandwidth scaling
factor may be selected dynamically in accordance with other criteria, such
as size of the patient and patient's arms, degree of alignment between
bone tissue in the arms and the cervical spine, alignment of other bone
tissue with the spine or other regions of the patient to be imaged,
compensation for other bone tissue adjacent regions of interest, and the
like. In views which include a high density object outside of the imaged
area, the high resolution and distance of the interfering object cause the
view sampling criterion to be violated. The bandwidth scale factor is
selected such that appropriate views within the given angular range and
location of the interfering objects are filtered sufficiently that the
filtered data meets the sampling criterion. This can be estimated in
advance based on the type of scan being conducted or may be calculated
from the currently collected data, data from the preceding adjoining
slice, or the like.
The noise texture means 46 selects bandwidth correction factors which
obtain a non-circularly symmetric point response function in the
reconstructed image. Higher order noise statistics or texture can be
altered without affecting the nominal noise and resolution measurements.
For example, reducing the bandwidth at 45.degree., 135.degree.,
225.degree., and 315.degree. while maintaining full bandwidth at
0.degree., 90.degree., 180.degree., and 270.degree. distorts a normally
circular noise texture by drawing it out at the corners (45.degree.,
135.degree., 225.degree., and 315.degree.) and holding it in at midpoints
(0.degree., 90.degree., 180.degree., 270.degree.) to approximate a square
or rectangle. A suitable bandwidth factor for achieving this noise texture
correction is:
BWF(.theta.)=(N.sub.T /N.sub.S).multidot..sqroot.(1+sin.sup.2
(2.theta.))(8).
When a circularly symmetric reconstruction kernel is used in the
reconstruction means 30, the filter function of Equation (8) gives an
asymmetric point response that is generally rectangular in form whose
nominal response, measured over 360.degree. is comparable to the original
image. A response of this nature may be particularly advantageous for
imaging on a rectangular matrix.
Analogously, other view dependent bandwidth scaling factors can be
selected. The bandwidth scaling factor selecting means 50 selects among
the bandwidth factors generated by each of the bandwidth factor selecting
means 40-48. In the preferred embodiment, the selected bandwidth scaling
factor BWF(.theta.) is the maximum value among the generated bandwidth
functions, i.e.:
BWF(.theta.)=MAX[BWF.sub.adaptive (.theta.),BWF.sub.missing views
(.theta.),BWF.sub.object (.theta.),BWF.sub.asymm (.theta.)](9).
In this manner, a single bandwidth scale factor as a function of the view
designation .theta. is provided.
The invention has been described with reference to the preferred
embodiments. It is intended that the invention be construed as including
all such alterations and modifications insofar as they come within the
scope of the appended claims or the equivalents thereof.
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